Abstract
The free convection boundary-layer flow of a Darcy–Boussinesq fluid from a vertical permeable plate with an inverse-linear temperature distribution is considered. The outstanding characteristics of this self-similar flow which, according to the usual reduction procedure of pseudo-similarity to full similarity, should not exist at all, are analyzed in detail. Thus it is shown that this flow only exists if a lateral suction with a sufficiently large suction parameter γ ≥ γmin = 1.079131 is applied. For the threshold value γmin the solution is unique but above it multiple solutions are encountered for every given value of γ.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Brouwers, H. J. H.: 1994, Heat transfer between a fluid-saturated porous medium and a permeable wall with fluid injection or withdrawal, Int. J. Heat Mass Transfer 37, 989-996.
Chaudhary, M. A., Merkin, J. H. and Pop, I.: 1995a, Similarity solutions in free convection boundary-layer flows adjacent to vertical permeable surfaces in porous media. I Prescribed surface temperature, Euro. J. Mech. Fluids 14, 217-237.
Chaudhary, M. A., Merkin, J. H. and Pop, I.: 1995, Similarity solutions in free convection boundary-layer flows adjacent to vertical permeable surfaces in porous media. II Prescribed surface heat flux, Heat Mass Transfer 30, 341-347.
Cheng, P.: 1977, The influence of lateral mass flux on free convection boundary layers in a saturated porous medium, Int. J. Heat Mass Transfer 20, 201-206.
Cheng, P. and Minkowycz, W. J.: 1977, Free convection about a vertical flat plate embedded in a porous medium with application to heat transfer from a dike, J. Geophys. Res. 82, 2040-2044.
Ingham, D. B. and Brown, I. N.: 1986, Flow past a suddenly heated vertical plate in a porous medium, Proc. Roy. Soc. London A 403, 51-80.
Ingham, D. B. and Pop, I. (eds): 1998, Transport Phenomena in Porous Media, Oxford, Pergamon.
Johnson, C. H. and Cheng, P.: 1978, Possible similarity solutions for free convection boundary layers adjacent to flat plates in porous media, Int. J. Heat Mass Transfer 21, 709-718.
Magyari, E. and Keller, B.: 2000, Exact analytic solutions for free convection boundary layers on a heated vertical plate with lateral mass flux embedded in a saturated porous medium, Heat Mass Transfer 36, 109-116.
Magyari, E., Ali, M. E. and Keller, B.: 2000, Boundary-layer flows induced by continuous surfaces stretched with rapidly decreasing velocities, Heat Mass Transfer (accepted for publication).
McNabb, A.: 1966, On convection in a porous medium, in: Proc. 2nd Australasian Conf. Hydraulics and Fluid Mech., University of Auckland, C161-171.
Merkin, J. H.: 1994, Natural-convection boundary-layer flow on a vertical surface with Newtonian heating, Int. J. Heat Fluid Flow 15, 392-398.
Nakayama, A. and Pop, I.: 1991, A unified similarity transformation for free, force and mixed convection in Darcy and non-Darcy media, Int. J. Heat Mass Transfer 34, 357-367.
Nield, D. A. and Bejan, A.: 1999, Convection in Porous Media, 2nd edn, Springer, New York.
Pop, I. and Takhar, H. S.: 1993, Free convection from a curved surface, J. Appl. Math. Mech. (ZAMM) 73, T534-T539.
Rosenau, P.: 1984, A note on integration of the Emden-Fowler equation, Int. J. Non-Linear Mech. 19 303-308.
Rosenhead, L.: 1963, Laminar Boundary Layers, Chapt. V, Sectin 21, Dover Publ, New York.
Sparrow, E. M. and Gregg, J. L.: 1958, Similar solutions for free convection from a non-isothermal vertical plate, Trans. ASME 80, 435-440.
Wright, S. D., Ingham, D. B. and Pop, I.: 1996, On natural convection from a vertical plate with a prescribed surface heat flux in porous media, Transp. in Porous Media 22, 181-193.
Wooding, R. A.: 1963, Convection in a saturated porous medium at large Rayleigh number or Péclet number, J. Fluid Mech. 15, 527-544.
Zaitsev, V. F. and Polyanin, A. D.: 1994, Discrete-group methods for integrating equations of snonlinear mechanics, CRC Press, Boca Raton.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Magyari, E., Pop, I. & Keller, B. The ‘Missing’ Self-Similar Free Convection Boundary-Layer Flow Over a Vertical Permeable Surface in a Porous Medium. Transport in Porous Media 46, 91–102 (2002). https://doi.org/10.1023/A:1013816831733
Issue Date:
DOI: https://doi.org/10.1023/A:1013816831733